To find the wavelength of violet light, we can use the wave equation:
\[ \text{wavelength} (\lambda) = \frac{\text{speed} (v)}{\text{frequency} (f)} \]
Given:
- Speed of light, \( v = 3.00 \times 10^8 \text{ m/s} \)
- Frequency of violet light, \( f = 7.26 \times 10^{14} \text{ Hz} \)
Substituting the values into the equation:
\[ \lambda = \frac{3.00 \times 10^8 \text{ m/s}}{7.26 \times 10^{14} \text{ Hz}} \]
Calculating the wavelength:
\[ \lambda \approx \frac{3.00}{7.26} \times 10^{8 - 14} \text{ m} = \frac{3.00}{7.26} \times 10^{-6} \text{ m} \]
Calculating \( \frac{3.00}{7.26} \):
\[ \frac{3.00}{7.26} \approx 0.412 \]
Now, substituting back:
\[ \lambda \approx 0.412 \times 10^{-6} \text{ m} = 4.12 \times 10^{-7} \text{ m} \]
To convert meters to nanometers, we can use the conversion \( 1 \text{ m} = 1 \times 10^{9} \text{ nm} \):
\[ \lambda \approx 4.12 \times 10^{-7} \text{ m} \times 10^{9} \text{ nm/m} \approx 412 \text{ nm} \]
Rounding to the nearest nanometer, the wavelength of violet light is:
\[ \lambda \approx 412 \text{ nm} \]
Thus, the final answer is:
412 nm
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